Journal of Finance and Accountancy Usefulness of expected values in liability valuation: the role of portfolio size Gary Colbert University of Colorado Denver Dennis Murray University of Colorado Denver Robert Nieschwietz Seattle University Abstract This study investigates whether the usefulness of expected values to financial statement users depends on portfolio size (N). Given that standard setting boards require some liabilities to be measured at fair value, and given that fair values are often estimated using expected cash flows, the investigation is conducted within the context of liabilities. Expected value is hypothesized to be more useful when N is large because actual cash flow realizations are more centered on their expected value than when N is small. That is, because users will perceive that expected values are more accurate predictors of actual realizations when N is large, valuations assigned to liabilities will be closer to their expected values than when N is small. The results show that when N is large, the valuations assigned by subjects to liabilities are much closer to the expected value of the future cash outflows than when N is small, but users’ perceptions of the accuracy of expected values did not appear to influence their valuations. These results suggest that standard setters should give consideration to the effect of portfolio size on the use of expected value in financial reporting. Keywords: Liability Valuation, Expected Value, Portfolio Size Usefulness of Expected Values, Page 1 Journal of Finance and Accountancy Introduction The Financial Accounting Standards Board (FASB) and the International Accounting Standards Board (IASB) have undertaken a joint project to reexamine their respective conceptual frameworks. The Boards hope that this reexamination will result in an improved and common framework. The project’s goals include updating the concepts to reflect new business practices and improving parts of the conceptual frameworks, such as the recognition criteria and measurement attributes of financial statement items (FASB 2006). The initial efforts by the Boards in this project have focused on the objectives of financial reporting and the qualitative characteristics of financial reporting information. The FASB has already published an exposure draft of two chapters addressing these issues (FASB 2008). The Boards are now directing their energies towards the two most fundamental financial statement elements: assets and liabilities. The FASB has issued an Invitation to Comment (FASB 2005) that is intended to solicit views regarding the central accounting issues associated with assets and liabilities. A critical aspect of accounting related to liabilities is the measurement attribute. That is, what measurement attribute should accountants assign to recognized liabilities? Accounting standards recently promulgated by the FASB have tended to require the use of fair value. For example, Statement of Financial Accounting Standard (SFAS) 143, Accounting for Asset Retirement Obligations (FASB 2001), and SFAS 146, Accounting for Costs Associated with Exit or Disposal Activities (FASB 2002) require that the liabilities addressed by those standards be stated at fair value. Further, SFAS 159, The Fair Value Option for Financial Assets and Financial Liabilities (FASB 2007), provides firms the option of valuing any financial liability at fair value. The IASB has taken a similar path. International Accounting Standard (IAS) 37, Provisions, Contingent Liabilities and Contingent Assets , (IASB 1998) requires that provisions (i.e., liabilities of uncertain timing or amount) be measured at the amount necessary to settle the liability on the balance sheet date. The FASB defines fair value as the price that would be paid to transfer a liability in an orderly transaction (FASB 2007). An observable marketplace-determined amount is often used in this regard. When observable marketplace-determined values are not available, the present value of future cash flows may be used. The FASB distinguishes between two types of future cash flow forecasts in Statement of Financial Accounting Concept (SFAC) 7, Using Cash Flow Information and Present Value in Accounting Measurements (FASB 2000). Estimated cash flow refers to the forecast of a single future cash flow amount and reflects the traditional approach to implementing present value. This amount usually reflects the most likely future cash flow (i.e., the best estimate). Expected cash flow refers to the probability-weighted sum of more than one possible forecasted cash flow realization. Given that the expected cash flow approach requires more explicit consideration of different assumptions and scenarios, the FASB has concluded that the use of the expected cash flow approach is preferable in many situations. SFAS 143, for example, states that “the expected cash flow approach will usually be the only appropriate technique for an asset retirement obligation” (FASB 2001, 8). The IASB also requires the use of expected value to measure liabilities in certain circumstances (IAS 37) and the Board is considering expanding the use of expected cash flow (IASB 2005). An example suggested in SFAC 7 raises an interesting issue related to the use of the expected cash flow approach. Consider a liability with two possible future cash flow realizations: a 90% probability of a $0 cash flow and a 10% probability of a $1,000 cash flow. Usefulness of Expected Values, Page 2 Journal of Finance and Accountancy The expected cash flow is $100. 1 Yet, this amount is not one of the possible future realizations. To what extent is it desirable to measure this liability based on an expected value that does not represent either of the possible realizations? 2 The lack of correspondence in this example between the expected value and future cash flow realizations arises, in part, due to the singular nature of the liability. That is, the example includes only one liability item. As the number of items in the portfolio (N) increases, the distribution of outcomes (i.e., the net result of multiple items) becomes increasingly concentrated around the expected value. As a result of the increased correspondence between the expected value and the realized outcomes, the expected value may prove to be more useful to financial statement users. Given that much of current GAAP requires, permits or recommends the use of expected cash flows to value liabilities in singular situations (e.g., SFAS 143, SFAS 146 and IAS 37), this paper investigates whether the usefulness of expected values to financial statement users depends on N. The participants in this study were asked to assign a settlement value to a hypothetical environmental contingency. It is hypothesized that the participants will assign a value that is closer to the expected value when N is large. The results show that when N is large, the valuations assigned by participants to liabilities are much closer to the expected value of the future cash outflows than when N is small. A causal model which hypothesizes that participants’ perceptions of accuracy intervene between N and the use of expected value is also tested. That is, when N is large expected value will be viewed as being a more accurate indicator of the ultimate cash outflow, and therefore, participants will assign settlement values closer to the expected value than when N is small. The results do not support the intervening role of accuracy perceptions. The remainder of this paper is organized as follows. The next section provides the motivation and hypotheses. The research method is discussed in the following section and the final two sections describe the results and provide a summary and conclusions. Motivation and Hypotheses Psychologists and management scientists have long been interested in studying how individuals make decisions under uncertainty. 3 This work, especially the work of Hogarth and Einhorn (1990) that models how individuals use probability information in risky decision making, is drawn on to formulate the hypotheses. Liability Portfolio Size Hogarth and Einhorn’s (1990) venture theory (VT) provides a descriptive model of outcomes individuals replace the associated probabilities of the outcomes with decision weights.4 1 ($0 X .9) + ($1,000 X .1) = $100. 2 Given that the focus is on the form of the cash flow forecasts, any discounting calculation is dispensed with in the remainder of the paper. 3 Much of this work was spawned by the seminal work of Kahneman and Tveresky (1979). 4 VT focuses on how probabilities are translated into decision weights. VT assumes that the associated payoff is transformed based on the value function of prospect theory (Kahneman and Tversky 1979). Usefulness of Expected Values, Page 3 Journal of Finance and Accountancy While it seems natural to use the probability of an outcome as a decision weight, Hogarth and Einhorn (1990) argue that this hides important psychological matters, particularly the effect of uncertainty. They reason that an individual’s intuition of probability is best equated with long- run, multiple-play, situations. Also, in multiple-play situations, because the realized outcome is likely near the expected value, expected value is more reflective of likely outcomes and the use of the stated probability of an outcome as a decision weight therefore corresponds to some reality. In contrast, they reason that when the number of plays is small expected value is less likely, and from a psychological point there is greater uncertainty. Hogarth and Einhorn refer to this additional uncertainty as outcome uncertainty. Hogarth and Einhorn (1990) model the decision process as an anchoring and adjustment process to arrive at decision weights. The initial anchor is the probability of the outcome provided and the adjustment, if any, is the result of a mental simulation that is affected by the presence of outcome uncertainty. The higher the outcome uncertainty the greater the extent of mental simulation and adjustment, increasing the likelihood of choices of decision weights that deviate from the probability provided. VT is used to formulate the hypothesis about the effect of liability portfolio size on individual’s valuation judgments.